Optimal growth and cycles in overlapping generations models

Abstract

This paper investigates the dynamical properties of optimal paths in one-sector overlapping generations models without assuming that the utility function of the representative agent is separable. When the utility function is separable, the optimal growth paths monotonically converges toward the modified golden rule steady state. In the non-separable case, we show that the optimal growth path may be oscillating and optimal two-period cycles may exist. Applying these results to the model with altruism, we show that the condition of operative bequest is fully compatible with endogeneous fluctuations provided that the discount factor is close enough to one. All our results are illustrated using Cobb-Douglas utility and production functions.